Let $y = y(x)$ be the solution of the differential equation $\dfrac{2 + \sin x}{y+1} \cdot \dfrac{dy}{dx} = -\cos x,\; y > 0,\; y(0) = 1.$ If $y(\pi) = a$ and $\dfrac{dy}{dx}$ at $x = \pi$ is $b$, then the ordered pair $(a,b)$ is equal to :

1

Let $X = \{x \in \mathbb{N} : 1 \leq x \leq 17\}$ and $Y = \{ax + b : x \in X,\; a \in \mathbb{R},\; b \in \mathbb{R…

Topic: JEE Main 2 September 2020 (Morning)

2

If $R = \{(x,y) : x,y \in \mathbb{Z}, \; x^{2} + 3y^{2} \leq 8 \}$ is a relation on the set of integers $\mathbb{Z}$, …

Topic: JEE Main 2 September 2020 (Morning)

3

Let $\alpha$ and $\beta$ be the roots of the equation $5x^2 + 6x - 2 = 0$. If $S_n = \alpha^n + \beta^n,\; n = 1,2,…

Topic: JEE Main 2 September 2020 (Morning)

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The domain of the function $f(x) = \sin^{-1}\!\left(\dfrac{|x|+5}{x^2+1}\right)$ is $(-\infty, -a] \cup [a, \infty)…

Topic: JEE Main 2 September 2020 (Morning)

5

$\left( \dfrac{1 + \sin\frac{2\pi}{9} + i \cos\frac{2\pi}{9}}{1 + \sin\frac{2\pi}{9} - i \cos\frac{2\pi}{9}} \right)^3$

Topic: JEE Main 2 September 2020 (Morning)

6

If p(x) be a polynomial of degree three that has a local maximum value 8 at x = 1 and a local minimum value 4 at x = 2;…

Topic: JEE Main 2 September 2020 (Morning)

7

The sum of the first three terms of a G.P. is S and their product is 27. Then all such S lie in :

Topic: JEE Main 2 September 2020 (Morning)

8

Let $A$ be a $2 \times 2$ real matrix with entries from $\{0,1\}$ and $|A|\neq 0$. Consider the following two statemen…

Topic: JEE Main 2 September 2020 (Morning)

9

Let $\alpha > 0, \, \beta > 0$ be such that $\alpha^3 + \beta^2 = 4$. If the maximum value of the term independent o…

Topic: JEE Main 2 September 2020 (Morning)

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If a function $f(x)$ defined by  $f(x) = \begin{cases} ae^x + be^{-x}, & -1 \leq x < 1 \\[6pt] cx^2, &amp…

Topic: JEE Main 2 September 2020 (Morning)